pob1212
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Hi,
True or False: Every infinite sequence of natural numbers, who's terms are randomly ordered, must contain every possible subsequence of any length, including infinity.
For example, does the infinite and random sequence \small M of natural numbers require that the subsequence {59,1,6} exist within it? Or the ordered set \small N of natural numbers for that matter?
My intuition is no. We could construct a sequence \small M, as described above, then extract every sequence {59,1,6} from \small M, and still have an infinite sequence. What about the idea that since M is infinite it has infinitely many chances for any unique set (even infinite sets like \small N) to occur within it?
Thanks,
pob
True or False: Every infinite sequence of natural numbers, who's terms are randomly ordered, must contain every possible subsequence of any length, including infinity.
For example, does the infinite and random sequence \small M of natural numbers require that the subsequence {59,1,6} exist within it? Or the ordered set \small N of natural numbers for that matter?
My intuition is no. We could construct a sequence \small M, as described above, then extract every sequence {59,1,6} from \small M, and still have an infinite sequence. What about the idea that since M is infinite it has infinitely many chances for any unique set (even infinite sets like \small N) to occur within it?
Thanks,
pob